Higher Dimensions
More general Heisenberg groups Hn may be defined for higher dimensions in Euclidean space, and more generally on symplectic vector spaces. The simplest general case is the real Heisenberg group of dimension 2n+1, for any integer n ≥ 1. As a group of matrices, Hn (or Hn(R) to indicate this is the Heisenberg group over the ring R or real numbers) is defined as the group of square matrices of size n+2 with entries in R:
where
- a is a row vector of length n,
- b is a column vector of length n,
- is the identity matrix of size n.
Read more about this topic: Heisenberg Group
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